Non-conductive heat transfer associated with frozen soils

Global and Planetary Change 29 Ž2001. 275–292 www.elsevier.comrlocatergloplacha

Non-conductive heat transfer associated with frozen soils Douglas L. Kane a,) , Kenneth M. Hinkel b,1, Douglas J. Goering c,2 , Larry D. Hinzman a,3, Samuel I. Outcalt b,4 a

Water and EnÕironmental Research Center, UniÕersity of Alaska Fairbanks, Fairbanks, AK 99775, USA b Department of Geography, UniÕersity of Cincinnati, Cincinnati, OH 45221, USA c Mechanical Engineering Department, UniÕersity of Alaska Fairbanks, Fairbanks, AK 99775, USA Received 18 May 1999; received in revised form 18 December 1999; accepted 4 May 2000

Abstract The assertion that pure conductive heat transfer always dominates in cold climates is at odds with decades of research in soil physics which clearly demonstrate that non-conductive heat transfer by water and water vapor are significant, and frequently are for specific periods the dominant modes of heat transfer near the ground surface. The thermal regime at the surface represents the effective boundary condition for deeper thermal regimes. Also, surface soils are going to respond more quickly to any climatic fluctuations; this is important to us because most facets of our lives are tied to earth’s surface. To accurately determine the surface thermal regime Žfor example, the detection of climate change., it is important to consider all potential forms of heat transfer. Gradients that have the potential to alter the thermal regime besides temperature include pore water pressure, gravitational, density, vapor pressure and chemical. The importance of several non-conductive heat transport mechanisms near the ground surface is examined. Infiltration into seasonally frozen soils and freezing Žrelease of latent heat. of water is one mechanism for the acceleration of warming in surficial soils in the spring. Free convection due to buoyancy-induced motion of fluids does not appear to be an important heat-transfer mechanism; estimates of the Rayleigh number Žthe ratio of buoyancy to viscous forces. are generally around 2, which is too low for effective heat transfer. The Peclet number Žratio of convective to conductive heat transfer. is on the order of 0.25 for snowmelt infiltration and up to 2.5 for rainfall infiltration for porous organic soils. In mineral soils, both vertical and horizontal advection of heat can be neglected ŽPeclet number is approximately 0.001. except for snowmelt infiltration into open thermal contraction cracks. The migration of water in response to temperature or chemical gradients from unfrozen soil depths to the freezing front, and the redistribution of moisture within the frozen soil from warmer depths to colder depths, can also result in heat transfer although this effect has not been quantified here. Many of these processes are seasonal and effective only during periods of phase change when the driving gradient near the ground surface is relatively large. q 2001 Elsevier Science B.V. All rights reserved. Keywords: non-conductive heat transfer; soils; infiltration; convection; phase change; climate

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Corresponding author. Tel.: q1-907-474-7808; fax: q1-907-474-7979. E-mail addresses: [email protected] ŽD.L. Kane., Ken – [email protected] ŽK.M. Hinkel., [email protected] ŽD.J. Goering., [email protected] ŽL.D. Hinzman., [email protected] ŽS.I. Outcalt.. 1 Tel.: q1-513-556-3421. 2 Tel.: q1-907-474-5059. 3 Tel.: q1-907-474-7331. 4 Tel.: q1-513-556-3421. 0921-8181r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 8 1 8 1 Ž 0 1 . 0 0 0 9 5 - 9

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1. Introduction A large fraction of the surficial soils in the world undergo seasonal freezing, with perennially frozen ground being common at higher, colder latitudes and in some mountainous areas. For a variety of scientific and engineering reasons, the prediction of soil temperature profiles and winter depth of freezing Žsummer depth of thaw in permafrost environments. have been pursued. Recently, ground temperature profiles have become important for reconstructing past climates Ždeep borehole profiles. and detecting recent climate change Žshallow borehole profiles.. A variety of techniques, ranging from simple empirical methods such as the degree–day method to complex, physically based conduction models have been utilized to address such problems. Discussed here are many non-conductive heat-transfer processes that are responsible for influencing surficial soil temperatures Žshallow borehole profiles. throughout the year. Non-conductive heat-transfer processes refer to all those physio-chemical processes not represented by the heat conduction equation. It should be noted that the surficial temperatures are also the effective upper boundary condition for the deeper temperature regime. The response of surficial soils to climate change will be subtle and may go undetected if all forms of heat transfer are not considered. This is particularly important in areas with extensive seasonal frost and those areas with continuous or discontinuous permafrost. Having the capability to predict near-surface temperatures in response to a changing climate is important for: determining the impact to the engineering infrastructure built on warm permafrost; evaluating the contribution of greenhouse gases to the atmosphere from decomposing organic soils; predicting how changes in evapotranspiration will affect agricultural production in semi-arid areas; and estimating changes in the hydrologic response of watersheds. Fourier Ž1822. published his classic paper on heat conduction entitled ATheorie Analytique de la ´ Chaleur.B Since then, it has been established that the major mechanism of heat transfer in soils is conduction, and models based on Fourier’s equation have been developed to adequately analyze a wide range of heat transfer problems. The history of Fourier’s heat conduction equation as a catalyst for the devel-

opment of other related relationships ŽOhm’s, Fick’s and Darcy’s laws. is reviewed in Narasimhan Ž1999.. Numerous applications of heat conduction theory to analyze borehole temperature data can be found in the literature. Lachenbruch and Marshall Ž1986. utilized solely heat conduction to analyze deep permafrost temperature profiles in an effort to reconstruct the thermal impact of climatic warming in the last century. They concluded that, AAlthough details of the climatic change cannot be resolved with existing data, there is little doubt of its general magnitude and timing; alternative explanations are limited by the fact that heat transfer in cold permafrost is exclusively by conduction.B In this case, the thickness Žseveral hundreds of meters. and cold surface temperatures Žcausing a reduction in the unfrozen water content. of the permafrost tend to limit the impact that non-conductive thermal processes may have. Still, it should be kept in mind that at the base of the permafrost, the temperature is at the freezing point and significant unfrozen water exist. Also, from the ground surface to the dampening depth Ždepth of minimum soil temperature. the direction of conductive heat transfer fluctuates seasonally. At the near surface, Nixon Ž1975. compared the role of vertical convective heat transfer caused by the migration of melt water to the thawing surface to conduction during soil thawing. He concluded that the impact of convective heat transfer was minor, although he did not allow for infiltration of water into the soil or for water to enter thermal cracks or other conveyances. When modeling surface permafrost temperatures, Nakano and Brown Ž1972. stated, AFrom a microscopic viewpoint, the mechanism of heat transport in soils is not by conduction alone. However, it is acceptable to define the effective conductivity of soils as the first approximation and to formulate the problem as one of pure conduction heat transfer as soil water undergoes phase changes.B Kane et al. Ž1991a. used a two-dimensional heat conduction model with phase change to illustrate how climatic warming would impact active layer Žthe layer of soil above permafrost that annually experiences freezing and thawing. temperatures and thaw depths. The model generally performed satisfactorily when compared with present conditions. However, each year during snowmelt, field temperatures were always warmer than predicted, thus indi-

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cating enhanced downward heat transfer during this period. Conduction theory is ideally suited to the analysis of rock bodies with uniform material properties throughout and no significant fluid movement. Although it is accepted that conduction accounts for a notable amount of the heat transfer in natural soils with varying material properties, there are other heat-transfer mechanisms in these porous soils Žwith the potential for water movement. that are active in defining the thermal regime of near-surface soils. Processes associated with the freezing and thawing of surficial soils, in both permafrost and non-permafrost regions, are of particular interest here. Frozen, unsaturated soils are difficult to model both hydraulically and thermally because of the many components that comprise the system: two solids Žsoil matrix and ice. and three fluids Žliquid water, air and water vapor.. Obviously, the number of components can be reduced if the system is thawed Žno ice. or if it is saturated Žno air or water vapor.. Air, water vapor and water are free to move within the soil matrix if appropriate gradients exist. If migration of these components does occur, the possibility of non-conductive heat transfer arises due to the associated transport of sensible or latent heat through the soil matrix. Unfrozen water films attached to the surface of soil particles in frozen soils allow water to move in the same direction as heat flow, from warmer to colder regions ŽHoekstra, 1966; Perfect and Williams, 1980.. The amount of unfrozen water is directly related to the soil temperature and texture, more specifically the surface area of soil particles ŽAnderson and Morgenstern, 1973.. For a given soil texture, colder soils have less unfrozen water. At the same temperature, soils with greater specific surface area Žsmaller particles. have higher unfrozen water contents. There are heat-transfer processes operating at all scales that, in addition to conduction, can significantly impact the thermal regime. Deming et al. Ž1992. found that near-surface heat fluxes on the North Slope of Alaska varied substantially across space, and attributed this variation to forced convection by a topographically driven regional groundwater flow system coupled with conduction. At a smaller scale Žusually a shallow volume surrounding a verti-

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cal string of temperature sensors in a shallow borehole., there is the possibility for a variety of nonthermal gradients to influence the thermal regime because of the smaller distances involved. It is possible for relatively large gradients to exist near the ground surface. Liquid water fluxes, which tend to be associated with heat fluxes in soils, can further complicate the thermal analysis, not so much because of the amount of advected heat involved but because of the large amount of latent heat available if phase change occurs. In addition to liquid movement and its contribution to phase change effects, there are a number of processes that involve the concurrent movement of both mass and energy. These are collectively referred to as Acoupled-flowB processes and entail the movement of water in the liquid andror vapor state ŽFarouki, 1981.. The driving force varies with the process. Rainwater and snowmelt infiltration is driven primarily by gravity and pore pressure gradients. Percolating water carries sensible heat downward Žcausing warming or cooling in the region through which it passes. with the releaseruptake of latent heat Žif there is an associated phase change.. The addition of water to a soil column alters the thermal properties, yielding a soil column where the heat capacity, thermal conductivity, and thus thermal diffusivity exhibit strong vertical and temporal variability ŽMcGaw et al., 1978; Hinkel et al., 1990..

2. Non-thermal gradients In addition to the thermal gradient used in Fourier’s conduction equation, there are several other gradients that may influence the near-surface thermal regime. Most of these gradients have a seasonal influence. In many studies, researchers use an effective thermal conductivity Žone that reproduces a measured thermal regime and incorporates non-conductive effects. rather than a thermal conductivity based purely upon heat conduction and determined experimentally in the laboratory or field. The purpose of this approach is to improve the simulation results, while simplifying the calculations by neglecting the explicit physical processes that are driven by other gradients. The following is a discussion of

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gradients that could impact coupled heatrmass transfer processes. 2.1. GraÕitational gradient The impact of the gravitational gradient is to partially control vertical water fluxes, which are important because of the sensible heat transfer and possibly latent heat. The gravitational gradient is always downward; however, it interacts with other seasonally dependent gradients that determine the net direction of water movement. During the fall and winter freeze-up, the gravitational gradient counteracts the upward movement of water toward the downward advancing freezing front. When water is drawn to the freezing front and subsequently freezes, latent heat of fusion is released. This impedes further advancement of the freezing front until this heat is dissipated. Conversely, during spring and summer, the gravitational gradient enhances snowmelt and rainfall infiltration. When meltwater from the overlying snowpack enters a soil with temperatures below the freezing point of bulk water, some of the water freezes with ensuing soil warming up to a maximum of 08C, while the remainder of the unfrozen water remains in equilibrium with the ice. 2.2. Pore water pressure gradient The pressure Žtension. of the film of water attached to the surface of a soil particle is a function of the moisture content and soil type. In saturated soils, moisture at the depth of the water table is at atmospheric pressure. As a soil dries, the pore water pressure above the water table becomes more negative Žsoil water suction. relative to atmospheric pressure. Water can also migrate in response to pore water pressure gradients generated at a freezing or evaporation front ŽWilliams and Smith, 1989.. In the case of a frozen soil, the formation of ice in a pore is comparable to drying a soil and the pore water pressure Žtension. increases negatively. As with the gravitational gradient, pressure gradients more strongly influence the migration of liquid water Žmass. than heat transfer Ženergy.. However, in contrast to the gravitational gradient that is always directed downward, pressure gradients can be directed

either up or down Žor even lateral.. In the absence of other operative gradients, the sum of the gravitational and the pore water gradients Ži.e., hydraulic gradient. dictates the ultimate direction of water flow. Assuming a homogeneous soil, the pore water pressure gradient is always in the direction from wet to dry soil. Where relatively impermeable, soil layers exist near the ground surface Žcoarser soil layer over clay layer or active layer over permafrost., water movement is typically restricted to a saturated region just above the impermeable layer, and in a direction that mimics the surface topography. 2.3. Osmotic (chemical) gradient As the soil begins to freeze downward, ions are excluded from the ice crystal lattice and increase the solute concentration of the soil water below the freezing front ŽHallet, 1978.. This activates soil physiochemical processes at depth. Development of a vertical osmotic gradient will cause water to move towards the zone of elevated solute concentration ŽHenry, 1988.. In a similar manner, the vapor pressure varies inversely with the exponential function of the solute concentration ŽPrutton and Maron, 1951.. Thus, a local increase in the soil water solute concentration, resulting from ion exclusion during ice growth or evaporative concentration, draws both vapor and liquid water towards the ion-enriched area. Because the processes of evaporation and freezing are seasonally dependent, the relative impact of coupled heatrmass flow processes on the soil thermal regime has a strong seasonal pattern. At temperatures well below freezing, these processes tend to cease due to large amounts of ice present in soil pores. However, at temperatures just below 08C, there is enough unfrozen water to allow these processes to remain active ŽMcGaw et al., 1978; Outcalt and Hinkel, 1996b.. 2.4. Density gradient Within a soil, it is possible to have a water or air density gradient that is generated by the temperature gradient. In this case, free convection can potentially occur when there are colder temperatures at the surface and relatively warmer temperatures at depth

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Žsometimes water but always air.. For water, free convection can occur in both the liquid and gas phases. During the summer, free convection does not occur because temperature typically decreases with depth and, therefore, the density of air increases with depth. Because the maximum density of water occurs near 48C, a typical soil temperature in cold regions, convection is somewhat more complicated in this temperature range. 2.5. Vapor pressure gradient Because of temperature differences, vapor pressure gradients exist in unsaturated soils. Such gradients result in water vapor concentration gradients within the pore air and, as a consequence, vapor diffusion will occur through the pores from warm to cold regions. In this way, vapor transport directly augments conductive heat transfer since the latent heat associated with moisture vapor movement is transported in the direction of the temperature gradient. Thermal conductivity measurements are often carried out using a guarded hot plate device that imposes a temperature gradient on a soil sample and accurately measures the resulting rate of heat transfer through the sample. Under these simplifying conditions, pressure and density gradients are minimal within the sample and convection is generally negligible. Heat is transferred through the sample via conduction through the soilrwaterrice matrix and, if the sample is in an unsaturated state, via moisture vapor transport in the open pore space. Experimental thermal conductivity measurements for moist soil will then necessarily include the influence of both soil matrix conduction and vapor transport Žaugmented slightly by sensible heat transfer by water movement on soil particle surfaces., as both mechanisms are active during measurement. Thus, the effective thermal conductivity measured in the laboratory essentially accounts for both soil matrix conduction and moisture vapor transport. Both of these processes are diffusive in nature and are driven by the temperature gradient, and as such, they can be combined using the effective thermal conductivity ŽGoering, 1991.. Even though vapor transport is a non-conductive process, the effects can be accounted

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for using a standard heat conduction model if vapor diffusion is largely driven by temperature gradients.

3. Phase change and boundary conditions In soils, a dominant energy storage term is phase change Žde Vries, 1974.. This entails the local liberation or consumption of energy associated with freezing or melting Ž0.33 MJ kgy1 ., evaporation or condensation Ž2.50 MJ kgy1 ., or sublimation Ž2.83 MJ kgy1 .. Although not directly accounted for in the heat conduction equation, phase change effects are typically incorporated into models of heat transfer in soils because these effects alter the soil enthalpy and change the soil physical and thermal properties ŽOutcalt, 1976; Goodrich, 1978.. Latent heat effects are particularly important during summer in Northern Alaska for the active layer, where up to 30–65% of the net solar energy is expended on evapotranspiration at the surface boundary ŽHarazono et al., 1995; Kane et al., 1990.. Latent heat effects are also important during freezing Žup to 4 months. or thawing Žthroughout the summer. of the active layer when there is associated phase change of ice and water. Also, for northern Alaska, Kane et al. Ž1990. found that over the summer, 15–17% of the net radiation was used for melting and warming the active layer. Rouse Ž1984. reported a similar value for a permafrost site in northern Canada. One clear example of phase change effects occurs in autumn when the active layer is freezing. The release of the latent heat of fusion acts to retard the penetration of the freezing front advancing from the surface downward and from the base of the active layer upward ŽSumgin et al., 1940; Outcalt et al., 1990.. This yields a depth or region in the active layer that is isothermal at or near 08C; this is referred to as the Azero-curtain.B This condition may persist for an extended period of time. Eventually, the soil water is converted to ice, the zero-curtain closes, and heat is removed more rapidly from the upper soil, primarily by conduction. During the period of zero curtain, the upper permafrost is effectively isolated from temperature variations at the soil surface due to the presence of the intervening isothermal active

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layer. This layer effectively attenuates the thermal signal. Convection, soil conduction, latent heat exchange Ževaporationrcondensation and freezingrthawing. and long and short wave radiation are fluxes that impact temperatures at the ground surface. Both vegetation and snow cover are effective buffers to these energy fluxes. In northern regions, it is common to have a layer of organic soils overlying mineral soils. Because the organic soils are porous and have relatively high hydraulic conductivities, they are very responsive to vertical infiltration and downslope water movement. This can result in rapid changes in the temperature at the organic–mineral soil interface during these episodic events. The thermal properties of these organic soils are highly dependent on moisture content. When dry, they form an effective insulator; when wet, an effective conductor. Changing surface conditions and varying properties Žand boundary conditions at soil interfaces. within soil layers are also important to the ground thermal regime. Annually, a snow cover presence Žessentially a change in boundary condition. for several months during the winter significantly alters the thermal conditions at the ground surface; the insulation of the overlying snow ŽGoodrich, 1982. moderates the subsurface soil temperatures. Warmer soils have more unfrozen water that enhances snowmelt infiltration. Similar thermal responses of the mineral soils beneath organic soils can be observed when the organic soils are relatively dry with high insulation values. In fact, the thermal conductivity of the surface organic layer varies significantly ŽHinzman et al., 1991. and is mainly dependent on soil density and moisture content.

4. Potential non-conductive heat transfer processes 4.1. Effects of Õapor transfer During summer, evaporation from the surface and within the active layer can significantly lower the mean summer temperature of the near-surface soil. Using a one-dimensional heat conduction model that incorporated the effects of fusion, Outcalt et al.

Ž1997, 1998. calculated temperatures in the active layer and upper permafrost and compared results to observed values. The residuals were typically negative during the daytime hours when evaporation was occurring. Because the upper probe Ž1 cm. temperature time series was used as a boundary condition, and the observed temperature incorporated the effects of evaporation, it was determined that the model still significantly underestimated the effects of evaporative cooling near the surface. An interesting example of non-conductive heat transfer where vapor transfer is thought to be an active process was observed in the active layer during the 1993 spring snowmelt at the Caribou–Poker Creeks Research Watershed near Fairbanks, Alaska. The taiga site is characterized by a thick Ž27 cm. layer of Sphagnum moss underlain by mixed Sphagnum duff and silt which extends to a depth of 41 cm; below this layer is colluvial silt. The permafrost table was at a depth of 47 cm. Hourly measurements of temperature and soil electric potential have been recorded since 1991. Eight high-resolution Ž0.0158C. probes were evenly spaced Ž7 cm apart. from the near-surface Ž1 cm. to a depth of 50 cm ŽFig. 1a and b.. The soil electric potential was used as a surrogate for the relative soil water solute concentration ŽOutcalt et al., 1990; Hinkel and Outcalt, 1994; Hinkel et al., 1997. and was used to derive a solute concentration index, or AC-indexB. Because the C-index spans several orders of magnitude during an annual cycle, the log of the C-index is used and referred to as ApCB in Fig. 1c. Higher values indicate a greater relative solute concentration at the probe level. Fig. 1a shows the hourly temperature at the eight probe levels during a 4-day period when two serial events Žsnowmelt related. occurred. In both cases, preferential warming occurred deep in the soil, but not at the surface, as would be expected in a purely conductive system. The thermal disruption was such that the temperature gradients were temporarily inverted. Furthermore, the hourly rate of warming was several orders of magnitude higher than observed in the previous several days. To examine these effects further, the first event has been isolated ŽFig. 1b and c. to show the temperature and pC traces, respectively, during a 24-h period. Prior to this, the soil was gradually warming

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Fig. 1. Hourly data from 1993 for Caribou–Poker Creek Research Center ŽCPCRC. near Fairbanks showing Ža. temperature record in upper 50 cm of soil for period 10–14 April, with symbols at 4-h interval and detail of warming event on 11 April showing Žb. temperature and Žc. log of C-index ŽpC. with symbols at 1-h interval.

and snowmelt was progressing. Note the sudden rise in temperature at the 36 cm level; with an increase of about 0.58C from 09:00 h Ždashed line. to 11:00 h, and an overall increase of about 0.758C over 5 h, this level becomes the warmest in the soil. A similar effect is observed at the 29- and 22-cm levels, although to a lesser degree. The C-index graph ŽFig. 1c. shows that the 36and 43-cm levels have the highest solute concentrations. This is consistent with closed system freezing

that yields a region near the base of the active layer that is enriched in solutes ŽHinkel and Outcalt, 1994; Hinkel et al., 1997; Outcalt and Hinkel, 1996b.. During the warming event, there is a reduction of the pC for the 36 cm depth at 09:00 h, which indicates solute dilution. A similar reduction is not measured at other depths. At a level of 36 cm, the rapid warming, combined with concurrent solute dilution in this zone of high solute concentration, indicates downward migration of water, either as vapor Žwith

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condensation. or as liquid. Vapor migration could be triggered by the addition of relatively pure solvent Žwater. at the surface generated by snowmelt and the osmotic gradient, or perhaps by snowmelt infiltration Ždiscussed later.. In the case of both snowmelt and rainfall infiltration, it appears that osmotic gradients augment both the gravitational and pore pressure gradients, forcing water downward into the soil. This is especially true of the early stages of infiltration, when relatively pure solvent is introduced at the soil surface. Vapor transport is not uncommon in porous and permeable materials such as organic-rich soils. Snow, too, demonstrates the effects of vapor transport during winter ŽSturm, 1991.. Vapor transport is very difficult to monitor ŽWoo, 1982; Smith and Burn, 1987., but there is clear evidence of vapor emission from soils and the production of hoar frost crystals at the base of the snowpack ŽMackay, 1983; Hinkel et al., 1996.. Porous organic soils often become desiccated in winter as coupled water and heat migrate upward through soil, through the snowpack, and into the atmosphere. Because the latent heat of condensation is so large, very little vapor is necessary to cause measurable warming. If we assume a bulk volumetric heat capacity of 2.25 J cmy3 Cy1 for the organic–silt–ice material, 0.6 mg of condensing water vapor per cmy3 will cause the temperature to increase 0.758C. 4.2. ConÕectiÕe heat transfer In general, two types of convective heat-transfer processes can occur. These include Ž1. forced convection that is driven by fluid pressure gradients, and Ž2. free convection that occurs as a result of temperature-induced variations in fluid density Žboth air and water.. Convection occurring in association with the movement of moist pore air or soil water can produce significant heat-transfer that is not driven directly by temperature gradients. As a consequence, it is generally not possible to account for these convective effects using a conduction-only model. 4.2.1. Free conÕection In a horizontal layer of porous material, such as an organic mat atop the active layer, free convection is most likely to occur during periods of cooling

from above. In this situation, cooling at the upper surface increases the density of the pore fluid, thereby generating unstable density stratification. If the density stratification is sufficient, free convection will ensue, with warmer pore fluid circulating up from beneath while the cooler pore fluid descends from above. The tendency for free convection to occur, and its strength, is a function of the Rayleigh number: Ra s

r 2 cg b KHDT mkm

Ž 1.

where r is the fluid density, c is the fluid heat capacity, g is the acceleration due to gravity, b is the thermal expansion coefficient for the fluid, K is the intrinsic soil permeability, H is the layer height, DT is the temperature difference across the layer, m is the dynamic viscosity of the fluid, and k m is the thermal conductivity of the soil. Nield and Bejan Ž1991. found that for an ideal horizontal system with planar boundaries, a critical Rayleigh number ranging between 3 and 39.5 Ždepending on boundary conditions. is theoretically required for free convection to occur. Sturm and Johnson Ž1991. observed free convection in undisturbed snow layers at Rayleigh numbers as low as 4. Within an active layer typical of arctic Alaska Žthe area of study in the present work., it is extremely unlikely that any free convection could occur in the mineral soil layer due to its relatively low permeability. The most likely possibility is that free convection associated with pore air movement would occur within the highly permeable surface organic mat during periods of strong wintertime cooling. Using Eq. Ž1., the maximum Rayleigh number is estimated to be approximately 2 for the organic mat typical of the Imnavait Creek watershed in arctic Alaska. This estimate is based on an organic mat thickness of 0.20 m, an intrinsic permeability of 2 = 10y1 1 m2 ŽHinzman et al., 1991., and the physical properties of the pore air. In consideration of the critical values discussed above, it is not likely that free convection would occur in such a system. Nevertheless, although advection velocities will be small, natural deviations from a planar horizontal system will generate some tendency for free convection to occur even at Rayleigh numbers below critical values; for example, hillslope topography can lead to

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instability at all Rayleigh numbers and result in upslope pore air motion through the organic mat during winter. Previous studies have shown that Rayleigh numbers on the order of 50 are required before the sensible heat advected by the moving pore air has an important impact on heat transfer ŽNield and Bejan, 1991.. In soil systems, however, even weak convection processes can produce significant heat transfer due to the fact that moist air is transported through the pore space. The inclusion of latent heat effects due to the advected water vapor Žassuming that the pore air remains in a saturated state as it travels. approximately doubles the energy transport over that produced by dry air convection alone. Even with the water vapor influence included, however, it is unlikely that significant heat transfer will result from free convection under the conditions described here. 4.2.2. Forced conÕection Forced convection associated with the movement of pore air or soil water may be important in soil systems, provided that significant pressure gradients are present in the active layer to drive the flow. In the case of pore air, forced convection may occur in the upper portion of the organic mat due to the influence of surface winds. This effect will be significant at depths below the surface that are less than the surface roughness length, and will usually be limited to the upper portions of the organic mat. From the modeling point of view, perhaps the largest impact of wind-induced pore–air convection will be associated with the establishment of boundary conditions at the surface of the active layer, rather than with enhanced heat transfer beneath the surface. Soil water flow due to gravitational, pore pressure, or osmotic pressure gradients ŽWegner, 1997. can also produce forced convection. These gradients can be effective at causing water movement in thawed as well as frozen soils, although flow rates are significantly reduced for the latter case. The impact of groundwater-induced convection can be assessed with the aid of the Peclet number that represents a non-dimensional ratio of convective to conductive heat transfer: Pe s

r cÕf lr km

Ž 2.

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where r and c are the density and specific heat of the moving fluid, Õf is the fluid velocity, l is the length scale over which heat transfer is occurring, k m is the thermal conductivity of the soil, and r is a length–scale ratio which must be included for cases where the convective and conductive processes occur over different length scales Žsuch as when comparing the importance of downslope convective effects with vertical conduction.. One limitation of the Peclet formulation shown above is that it is based on the advection of sensible heat, and does not include any consideration of advected latent heat. The contribution of latent heat can be very important if, for instance, liquid water is advected into a location of frozen soil where it subsequently re-freezes. In such cases, liberation of latent heat release increases the impact of soil water convection by approximately an order of magnitude. The possible impact of forced convection due to soil water flow can be estimated for conditions typical of the Imnavait Creek watershed. This watershed has slopes of approximately 10% that lead from the watershed divides approximately 500 m downslope to the creek in the valley bottom. Maximum active layer thickness is in the order of 0.50 m within the watershed, although significant variation in this thickness exists. Active layer soils generally consist of an upper organic mat with a thickness of approximately 0.20 m and of relatively low bulk density. The organic mat is underlain by wet glacial outwash silts with a porosity of about 0.5. Thermal conductivity values are approximately 1 Wrm K for the mineral soils and about half this for the organic soils Ždepending on moisture content.. The hydraulic conductivity of the mineral soil layer is in the order of 1 = 10y5 mrs while the value for the organic mat is approximately 20 times this value ŽHinzman et al., 1991.. Although water migration through the soil can occur in response to pore pressure and osmotic and gravitational gradients, it is likely that the highest flow velocities will occur in response to gravitational gradients associated with large infiltration events during spring snowmelt and summer rains. For the Imnavait watershed, estimates of maximum infiltration rates are 1 = 10y2 mrh for intense rain events and 0.1 = 10y2 mrh for snowmelt ŽKane et al., 1991b, 1989.. Using these infiltration rates, in com-

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bination with the thermal and hydraulic properties described above, it is possible to approximate the Peclet number for several flow scenarios and thereby provide an estimate of the impact of convective heat transfer due to moving groundwater. 4.2.3. Process comparisons Three specific process comparisons are made for both the organic mat and the mineral soil layer. The first two describe the relative importance of vertical convection due to infiltrating rain or snowmelt water versus thermal conduction in the vertical direction. In each case, the comparison is based on a Peclet number calculated using Eq. Ž2. with the appropriate material properties, vertical flow velocities, and length scales. Due to the large hydraulic conductivity of the organic mat, it was assumed that any water added at the surface would immediately infiltrate through the layer and, therefore, the vertical infiltration velocity can be taken as equal to the water generation rate at the surface Žsee values above.. Utilizing these assumptions, Peclet numbers for rain and snowmelt infiltration have been calculated and appear as Cases 1 and 2, respectively, in Table 1. A third comparison was carried out in order to judge the importance of horizontal Ždownslope. water flow. In this case, a Peclet number comparing the relative importance of horizontal convection and vertical conduction was formulated. Since the horizontal and vertical length scales are different for these processes Ž500 m horizontal vs. 0.50 m vertical., the length scale ratio Ž r in Eq. Ž2.. was set to 0.001 for this calculation. The downslope flow velocity was based on the hydraulic conductivity and slope values given above. The Peclet number for this situation is labeled Case 3 in Table 1.

The results shown in Table 1 indicate that intense rain events should produce vertical water movement in the organic mat that is significant in terms of the associated convective heat transfer. The Peclet number for this case is substantially larger than 1.0, indicating that thermal convection associated with infiltration will be the dominant heat transfer mechanism during these episodic summer events. For Case 2 and particularly for Case 3, convection plays a less important role. Snowmelt infiltration produces a Peclet number of 0.25, which indicates that conduction will be the dominant heat-transfer mechanism during snow ablation. This convective component will have a small but perhaps significant impact on the thermal regime. Case 3 indicates that downslope movement of water through the organic mat has an insignificant impact on heat transfer. In addition to the results shown in Table 1 for the organic mat, a similar set of numbers has been formulated for the mineral soil layer typical of the Imnavait Creek watershed. Note that vertical convection in the mineral soil is less likely than it is in the organic mat because the mineral soil remains near saturation for most of the summer period. Consequently, water entering the system at the ground surface generally runs downslope within the organic mat or via overland flow, instead of infiltrating into the mineral soil layer. Nevertheless, Peclet numbers in Table 2 for the mineral soil layer are based on the same assumption of complete vertical infiltration in the case of rain or snowmelt events used previously for the organic mat. This assumption is supported by the work of Kane and Stein Ž1983., who observed infiltration velocities during snowmelt approaching 1 = 10y2 mrh, even when the soils were in a frozen state.

Table 1 Peclet numbers for the organic mat

Table 2 Peclet numbers for the mineral soil layer

Process comparison

Peclet number

Process comparison

Peclet number

Case 1: Vertical Convectionr Vertical Conduction ŽRain. Case 2: Vertical Convectionr Vertical Conduction ŽSnowmelt. Case 3: Horizontal Convectionr Vertical Conduction

; 2.5

Case 4: Vertical Convectionr Vertical Conduction ŽRain. Case 5: Vertical Convectionr Vertical Conduction ŽSnowmelt. Case 6: Horizontal Convectionr Vertical Conduction

;1.2

; 0.25 ; 0.04

; 0.12 ; 0.001

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Table 2 shows that the Peclet numbers are smaller for mineral soils than for the organic mat. This is due to a combination of smaller hydraulic conductivity and larger thermal conductivity, each of which tends to reduce the importance of forced convection. In this case, although the results indicate that vertical convection due to infiltrating rainwater can have significant heat-transfer effects Žapproximately equal to conductive effects., snowmelt infiltration or downslope water flow can be largely neglected in terms of heat transfer. However, it should be noted that these conclusions are based on conditions in the Imnavait Watershed and Peclet numbers may have to be re-evaluated if conditions vary significantly from those described here. One final point concerning the results shown in Tables 1 and 2 relates to the fact that the Peclet number formulation ŽEq. Ž2.. includes only the effect of advected sensible heat. Under certain circumstances, the impact of latent heat may become important and the convective effect can be greatly amplified. As stated previously, latent heat effects will increase the impact of convection via soil water movement by approximately an order of magnitude and will, therefore, increase the associated Peclet number by the same factor. With this in mind, it is suggested that Cases 1, 2, 4 and 5 from Tables 1 and 2 will all produce significant Žperhaps dominant. convective heat-transfer effects if latent heat becomes important. The most likely scenario for this to occur would involve infiltration of snowmelt into a zone of sub-zero frozen soil. In this case, we would

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expect rapid freezing of some or all of the advected water, releasing large amounts of latent heat and producing relatively rapid warming of the soil matrix to 08C, as demonstrated in the next section. Groundwater movement can also have an impact on the thermal regime of the active layer in ways unrelated to convective heat transfer. In permafrost environments, water moves downslope through the active layer in water tracks, or areas of enhanced soil moisture ŽKane et al., 1989; Hastings et al., 1989., that act as contributing areas for runoff generation ŽMcNamara et al., 1999.. Field observations of the active layer depth indicate that thawing at these sites is enhanced. For example, Fig. 2 illustrates that the average depth of thaw is about 50% greater in the vicinity of water tracks than in inter-water track areas. However, Cases 3 and 6 Žshown in Tables 1 and 2. imply that this increased thaw depth is not due to convection. An explanation lies in the fact that the thermal properties of the surface organic mat are a strong function of moisture content. In water track areas, the organic mat remains in a saturated state for most of the summer season; thus it has an enhanced thermal conductivity compared to interwater track areas. This enhanced thermal conductivity effectively supplies a warm boundary condition for the upper surface of the mineral soil layer, thereby producing enhanced thaw in these locations. In the following sections, specific data sets are presented that illustrate convective heat transfer effects associated with snowmelt and rainfall infiltration. In each case, temperature and C-index data are

Fig. 2. Schematic of a hillslope cross-section between two water tracks with the average depth of thaw shown for the water track and better drained inter-water track Ž D IT s depth of thaw for inter-track, D WT s depth of thaw for water track..

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Fig. 3. Average daily values for Happy Valley site for period 13 August 1997 to 13 August 1998 showing Ža. temperature and Žb. pC in upper soil. ZC and SM refer to Azero-curtainB and AsnowmeltB, respectively. FR implies freezing.

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analyzed in order to assess the characteristics of the downward advection of surface water and the concomitant convective heat transfer. 4.3. Snowmelt infiltration example Water generated by melting snow can percolate down through soil pores or thermal contraction cracks ŽStein and Kane, 1983.. This has been demonstrated at several sites in taiga ŽHinkel and Outcalt, 1994; Hinkel et al., 1997. and tundra ŽOutcalt and Hinkel, 1996a; Hinkel et al., 1997. terrain. The process is most effective in open-textured soils with pores unoccupied by water or ice; conditions that occur most often in well-drained mineral and organic soils. The following example comes from an area located in Happy Valley, Alaska, in the northern foothills of the Brooks Range. This tundra site is characterized by tussock vegetation, with organic soils overlying silt of aeolian origin.

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Fig. 3 shows the average daily soil temperature and C-index for the period mid-August 1997 to mid-August 1998; these are derived from hourly values. The array of eight small probes was installed at depths of 1, 8, 15, 22, 29, 50, 75 and 100 cm in August 1993. The thermistor resolution is - 0.158C. Only the upper five pC traces are shown in Fig. 3b as others have been omitted for graph clarity. At this site, a 0.16-m thick organic layer overlies loess. The active layer is about 0.35 m thick, and both the active layer and upper permafrost are highly cryoturbated with fingers of organics throughout the loess and extending below the base of the active layer. Clear, massive segregation ice is encountered beginning at 0.39 m and extending to a depth exceeding 1.10 m. Figs. 3 and 4 also show the extended duration of the zero-curtain Žlabeled ZC., which persists for 6–8 weeks at this site. The role of latent heat in retarding penetration of the freezing front was discussed ear-

Fig. 4. Hourly temperature change Ž DT, 8C hy1 . at 8-cm probe level for period of record shown in Fig. 3.

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lier, and additional details are available from Hinkel et al. Ž2001.. Notice the increase in the pC ŽFig. 3b. just prior to closure of the zero curtain in December ŽFig. 3a., the sharp reduction of pC with soil freezing ŽFig. 3b, FR., and the rapid dilution Žreduction of pC. during the short snowmelt event ŽFig. 3b, labeled SM.. The pC tends to increase in summer due to evaporative concentration, and demonstrates variations associated with synoptic weather events. Fig. 4 shows the hourly temperature change DT Ž8C hy1 . at the 8 cm level for the period of 1 year. Positive values occur during daily soil warming and negative values are associated with nocturnal soil cooling. This yields the pattern of two sets of parallel traces that are mirrored across DT s 08C. The subparallel Žinside. traces are at the resolution of the thermistor, which improves with a temperature decrease in winter. The temporal pattern is the same at the other probe levels within the active layer, although the magnitude of DT decreases with depth. Note the thermal activity in the summer and, by

contrast, the thermal quiescence Ž DT s 08C. during the period of the zero-curtain. Observe the cluster of data points caused by the large-magnitude positive Žwarming. event in mid-May, 1998. These clusters occur in response to snowmelt infiltration ŽSM. and occur throughout the soil column to the depth of the 29-cm probe. The largest magnitude event Žq1.38C. occurs in late June and is associated with a rainfall event. It can be seen from this data that there is only a positive component Ženergy added to the system. for both the snowmelt and rainfall events. Fig. 5 shows hourly temperature data for the period 6–22 May 1998, and illustrates three snowmelt infiltration events on 10, 11 and 15 May. Note the step-like increase in temperature during these events and the disruption of the thermal gradients. These events are associated with the large positive DT values in Fig. 4. Snow had melted by 19 May Žas demonstrated in Fig. 3.; after this date, the abovefreezing diurnal cycle occurred at the 1-cm level. In the soil zone between 8 and 22 cm, note the com-

Fig. 5. Hourly temperature record at Happy Valley for 16-day period in May 1998 during snowmelt. Symbols are at 12-h interval.

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plete absence of the diurnal signal and the isothermal soil condition from 15 to 19 May. During the 10 May event, infiltration in midmorning had maximum impact at the 8, 15 and 22 cm levels with a temperature increase of about 28C over several hours. During this period, the temperature at the 22-cm probe level was warmer than the soil above, yielding a thermal inversion typical of infiltration events. The pre-event thermal gradients were largely re-established by the end of the day. During this event, conductive warming was observed at the 29, 50 and 75 cm levels Žthe latter two levels are within segregation ice, a relatively good conductor.. Step increases are often observed during the spring melt and are especially pronounced in porous soils ŽHinkel and Outcalt, 1993, 1997.. A similar effect is also observed in the data record from Barrow, Alaska, but the impact is much reduced because the pore space in the reworked silt is nearly saturated with

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ice, effectively blocking the pores and preventing downward water movement ŽHinkel et al., 2001.. Fig. 6 details the infiltration event of 15 May. The impact is similar to—but more pronounced than—the previous events. Near-surface warming in the morning is disrupted by snowmelt infiltration. The maximum change is measured at the 29-cm level, where the temperature increases 3–48C in 2 h. By midafternoon, the soil is isothermal near 08C in the region above the segregation ice layer at 39 cm. This suggests subsurface flooding and saturation in a porous, permeable soil. The rapidity of the event suggests infiltration through the frozen soil, possibly through micro-cracks caused by thermal contraction and desiccation in winter. Infiltration through cracks also explains the occurrence of vertical ice veins in the active layer Že.g. Shur et al., 1995. and possibly the 5% increase in ice content in the upper permafrost at Barrow over a period of 30 years ŽHinkel et al., 1996..

Fig. 6. Detail of temperature record at Happy Valley for 15 May 1998. Symbols are at 1-h interval.

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The above results can be compared with modeled results of Kane et al. Ž1991a., in which a heat conduction model with phase change was used to predict soil temperatures at Imnavait Creek, Alaska, a site similar to the nearby Happy Valley site. Over the 4-year simulation, predicted temperatures were always several degrees less than measured temperatures for a 2–3 week period during snowmelt. 4.4. Rainfall infiltration example The thermal impact of rainfall infiltration has been described elsewhere ŽHinkel et al., 1993, 1997., and it appears to be most effective in well-drained and organic soils. At the Caribou–Poker Creeks Research Watershed, a well-documented event occurred in mid-August 1991 when 71 mm of rain fell over a 24-h period. Pooling of the water above the permafrost caused the entire soil profile between 8 and 22 cm to become isothermal at 48C, and the C-index to become equivalent at all levels. The hourly data were of sufficient temporal resolution to observe the upward saturation of the active layer during the event. Enhanced melting at the base of the active layer caused a significant deepening as sensible heat was transferred to depth. A similar pattern was observed in 1993 at a boreal forest site near the Martin River in Western Canada; in this case, the rate of warming was 1–2 orders of magnitude greater than that observed when purely conductive processes were operating ŽHinkel et al., 1997..

Free convection in mineral soils is not possible because of their low permeability. Surface organic soils from the North Slope of Alaska have a Rayleigh number of about 2.0, too low for effective heat transfer. During snowmelt, the ratio of the convective to conductive heat transfer ŽPeclet number. is typically low, around 0.25. However, the infiltration of water into soils at temperatures below the freezing point of bulk water results in refreezing and the immediate release of latent heat. This process results in rapid warming of the soil to 08C. Surface organic soils with low bulk density and high porosity are good thermal insulators, but permeable to the movement of fluids. Vertical convective heat transfer during rain events can be significant ŽPeclet number up to 2.5., but these events are short duration episodic events. Water movement down slopes of enhanced soil moisture levels underlain by permafrost Žwater tracks. results in deeper thaw depths. Advected heat transfer is minimal in this case; due to the influx of water, the thermal conductivity is higher. While many of these non-conductive processes result in a warmer soil profile or deeper active layer at summer’s end, some Žlike evaporative cooling. result in just the opposite conditions. The importance of each of these non-conductive processes depends upon local site conditions that are highly variable. Other heat transfer processes Žsuch as osmotic. that are possible have little impact, although they have not been quantified for natural systems in this paper.

5. Conclusions

Acknowledgements

Most analyses of heat transfer in frozen soil systems have assumed that heat flow is solely by conduction—in many cases a good assumption. There are, however, many processes involving the movement of fluids into and within frozen soils that could be important to the thermal regime, especially near the ground surface. The spring and fall transition periods, when phase change is occurring within the surficial soils, are very important in terms of the soil thermal regime. The development of isothermal conditions Žzero curtain. through the release of latent heat during freezing results in negligible vertical thermal gradients and the suppression of heat transfer by conduction.

The research described in this paper was made possible through support provided by the National Science Foundation, Office of Polar Programs, Arctic Systems Science, grants OPP-9318535, OPP9814984, OPP-9529783 and OPP-9732051. We would like to thank Diana Allen and an anonymous reviewer for their excellent review comments.

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